Problem: Which of the following numbers is a factor of 194? ${2,5,6,9,10}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $194$ by each of our answer choices. $194 \div 2 = 97$ $194 \div 5 = 38\text{ R }4$ $194 \div 6 = 32\text{ R }2$ $194 \div 9 = 21\text{ R }5$ $194 \div 10 = 19\text{ R }4$ The only answer choice that divides into $194$ with no remainder is $2$ $ 97$ $2$ $194$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $194$ $194 = 2\times97 2 = 2$ Therefore the only factor of $194$ out of our choices is $2$. We can say that $194$ is divisible by $2$.